Stationary solution to the fluid queue fed by an M/M/1 queue

We consider an infinite-capacity buffer receiving fluid at a rate depending on the state of an M/M/1 queue. We obtain a new analytic expression for the joint stationary distribution of the buffer level and the state of the M/M/1 queue. This expression is obtained by the use of generating functions w...

Full description

Saved in:
Bibliographic Details
Published in:Journal of applied probability 2002-06, Vol.39 (2), p.359-369
Main Authors: Barbot, N., Sericola, B.
Format: Article
Language:English
Subjects:
60J27
60K25
Exact sciences and technology
Fluid queue
Generating function
generating functions
M/M/1 queue
Markov chains
Markov processes
Mathematical models
Mathematics
Modeling
Probability
Probability and statistics
Probability theory and stochastic processes
Queuing
Research Papers
Sciences and techniques of general use
Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)
Studies
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider an infinite-capacity buffer receiving fluid at a rate depending on the state of an M/M/1 queue. We obtain a new analytic expression for the joint stationary distribution of the buffer level and the state of the M/M/1 queue. This expression is obtained by the use of generating functions which are explicitly inverted. The case of a finite capacity fluid queue is also considered.
ISSN:0021-9002
1475-6072
DOI:10.1239/jap/1025131431